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Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing

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  • Jean-Marie Dufour

    ()

  • Tarek Jouini

Abstract

Statistical tests in vector autoregressive (VAR) models are typically based on large-sample approximations, involving the use of asymptotic distributions or bootstrap techniques. After documenting that such methods can be very misleading even with fairly large samples, especially when the number of lags or the number of equations is not small, we propose a general simulation-based technique that allows one to control completely the level of tests in parametric VAR models. In particular, we show that maximized Monte Carlo tests [Dufour (2005, Journal of Econometrics)] can provide provably exact tests for such models, whether they are stationary or integrated. Applications to order selection and causality testing are considered as special cases. The technique developed is applied to quarterly and monthly VAR models of the U.S. economy, comprising income, money, interest rates and prices, over the period 1965-1996. Les tests statistiques sur des modèles autorégressifs multivariés (VAR) sont habituellement basés sur des approximations de grands échantillons, qui utilisent une loi asymptotique ou une technique de bootstrap. Après avoir montré que ces méthodes peuvent être très peu fiables, même avec des échantillons de taille assez grande, particulièrement lorsque le nombre des retards ou le nombre d’équations augmentent, nous proposons une technique générale basée sur la simulation qui permet de contrôler parfaitement le niveau des tests dans les modèles VAR paramétriques. En particulier, nous montrons que la technique des tests de Monte Carlo maximisés [Dufour (2005, Journal of Econometrics)] fournit des tests exacts pour de tels modèles, que ceux-ci soient stationnaires ou intégrés. Sélectionner l’ordre du modèle ainsi que tester la causalité au sens de Granger sont étudiés comme problèmes particuliers dans ce cadre. La technique proposée est appliquée à des modèles VAR, trimestriels et mensuels, de l’économie américaine, comprenant le revenu, la monnaie, un taux d’intérêt et le niveau des prix, sur la période 1965-1996.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2005s-26.

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Date of creation: 01 Aug 2005
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Handle: RePEc:cir:cirwor:2005s-26

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Keywords: bootstrap; exact test; Granger causality; inflation; interest rate; macroeconomics; maximized Monte Carlo test; money and income; Monte Carlo test; nonstationary model; order selection; VAR; vector autoregression; autorégression vectorielle; bootstrap; causalité au sens de Granger; inflation; macroéconomie; modèle non-stationnaire; monnaie et revenu; sélection de l’ordre; taux d’intérêt; test exact; test de Monte Carlo; test de Monte Carlo maximisé; VAR;

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Cited by:
  1. DUFOUR, Jean-Marie, 2005. "Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics," Cahiers de recherche 03-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Jonathan B. Hill, 2005. "Causation Delays and Causal Neutralization up to Three Steps Ahead: The Money-Output Relationship Revisited," Econometrics 0503016, EconWPA, revised 23 Mar 2005.
  3. Jonathan B. Hill, 2004. "Efficient Tests of Long-Run Causation in Trivariate VAR Processes with a Rolling Window Study of the Money-Income Relationship," Working Papers 0413, Florida International University, Department of Economics.
  4. Jonathan B. Hill, 2004. "Causation Delays and Causal Neutralization: The Money-Output Relationship Revisited," Working Papers 0403, Florida International University, Department of Economics.

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